A bidomain model for anisotropic cardiac muscle

Abstract

Cardiac muscle is considered to consist of an intracellular domain and an exracellular or interstitial domain. Current passes from one domain to the other through the cell membrane. Electric potentials in interstitial space are shown to be associated with current sources proportional to the spatial gradient of the cellular transmembrane action potential, φ _m . Hence, given the distribution of φ _m throughout the myocardium, one can calculate the surface electrocardiogram and extracorporeal magnetocardiogram. The problem is considerably complicated when anisotropy is considered. If interstitial space is approximately isotropic, however, the sources are still proportional to ∇φ _m . It is shown that the effects of intracellular anisotropy on the surface electrocardiogram may be relatively small. The inverse problem is discussed briefly, with consideration of the relationship of the magnetocardiogram to the electrocardiogram. Finally, it is shown that if the heart can be considered to be bounded by a closed surface, then the value of φ _m on this surface is uniquely related to the surface electrocardiogram to within a constant, provided there are no internal discontinuities. Such discontinuities, however, would be expected to occur in cases of ischemia and necrosis.